Advanced Specialization

While a graduate student at Arizona State University, I researched, developed, and proved a technique for deriving implementable, near-optimal, direct sampled-data controllers for multiple-input/multiple-output distributed-parameter systems.

This research has direct applicability to the centralized and shared sampled-data control, in the presence of time-delays, of a large array of MEMS based optical crossconnect (OXC) reflectors which are the basis of some optical internet architectures.

The motivation for this research is the need for lower cost, reconfigurable, and better performing systems which lead naturally to control system design methods based on accurate system descriptions and microprocessor based control. The "accurate" system description may be in terms of continuous-time partial differential equations or involve time-delays. The continuous-time plant, discrete-time controller combination results in a sampled-data control system. To be implemented within the microprocessor, the controller must be finite-dimensional.

The typical engineering approach to synthesizing such a controller is to approximate the continuous-time infinite-dimensional plant by a continuous-time finite-dimensional model and to design a continuous-time finite-dimensional controller based on this model. This controller is then discretized using one of the various discretization methods to yield a sampled-data controller, which can then be implemented within the microprocessor.

The drawbacks to this approach, which is referred to as the Approximate/Design (Indirect) approach, are that intersample signal behavior isn't directly accounted for during sampled-data controller synthesis and there's no guarantee that the resultant closed-loop sampled-data system will be stable much less satisfy performance requirements. These shortcomings are partially compensated for by using a conservative (high) sample-rate. This, however, reduces the amount of processor time allocatable to other critical functions such as fault diagnostics and health monitoring.

To ameliorate the previously described shortcomings associated with the typical engineering (Approximate/Design) approach, the following research objective was established:

Derive a finite-dimensional sampled-data controller synthesis methodology, based on approximants of the infinite-dimensional plant that delivers near-optimal performance with intersample behavior included. Method to include sample-rate as a design parameter, as well as, a priori computable conditions on the approximants.

The documentation of the work performed in satisfying the research objective is listed below as PDF files. There you will find links to the initial thesis proposal (0.2 MB) documenting in further detail the validity and usefulness of this research, the complete thesis research dissertation (4.0 MB) containing thesis proof results and examples, and the presentation given in defense of the thesis research dissertation (1.4 MB).


Research Proposal

Thesis Dissertation

Thesis Defense


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